In several previous publications the first author has proposed a "generalized likelihood function" (GLF) approach
for processing nontraditional measurements such as attributes, features, natural-language statements, and inference
rules. The GLF approach is based on random set "generalized measurement models" for nontraditional
measurements. GLFs are not conventional likelihood functions, since they are not density functions and their
integrals are usually infinite, rather than equal to 1. For this reason, it has been unclear whether or not the
GLF approach is fully rigorous from a strict Bayesian point of view. In a recent paper, the first author demonstrated
that the GLF of a specific type of nontraditional measurement-quantized measurements-is rigorously
Bayesian. In this paper we show that this result can be generalized to arbitrary nontraditional measurements,
thus removing any doubt that the GLF approach is rigorously Bayesian.